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ACCRETION VARIABILITY OF HERBIG Ae/Be STARS OBSERVED BY X-SHOOTER HD 31648 AND HD 163296
I. Mendigut´ıa1, S. Brittain1, C. Eiroa2, G. Meeus2, B. Montesinos3, A. Mora4, J. Muzerolle5, R. D. Oudmaijer6, and E. Rigliaco7
1Department of Physics and Astronomy, Clemson University, Clemson, SC 29634-0978, USA;[email protected]
2Departamento de F´ısica Te´orica, M´odulo 15, Facultad de Ciencias, Universidad Aut´onoma de Madrid, P.O. Box 78, E-28049, Cantoblanco, Madrid, Spain
3Centro de Astrobiolog´ıa, Departamento de Astrof´ısica (CSIC-INTA), ESAC Campus, P.O. Box 78, E-28691 Villanueva de la Ca˜nada, Madrid, Spain
4GAIA Science Operations Centre, ESA, European Space Astronomy Centre, P.O. Box 78, E-28691, Villanueva de la Ca˜nada, Madrid, Spain
5Space Telescope Science Institute, 3700 San Martin Drive, Baltimore, MD 21218, USA
6School of Physics & Astronomy, University of Leeds, Woodhouse Lane, Leeds LS2 9JT, UK
7Department of Planetary Science, Lunar and Planetary Lab, University of Arizona, 1629, E. University Boulevard, 85719, Tucson, AZ, USA Received 2013 May 20; accepted 2013 August 13; published 2013 September 24
ABSTRACT
This work presents X-Shooter/Very Large Telescope spectra of the prototypical, isolated Herbig Ae stars HD 31648 (MWC 480) and HD 163296 over five epochs separated by timescales ranging from days to months. Each spectrum spans over a wide wavelength range covering from 310 to 2475 nm. We have monitored the continuum excess in the Balmer region of the spectra and the luminosity of 12 ultraviolet, optical, and near-infrared spectral lines that are commonly used as accretion tracers for T Tauri stars. The observed strengths of the Balmer excesses have been reproduced from a magnetospheric accretion shock model, providing a mean mass accretion rate of 1.11× 10−7 and 4.50× 10−7Myr−1for HD 31648 and HD 163296, respectively. Accretion rate variations are observed, being more pronounced for HD 31648 (up to 0.5 dex). However, from the comparison with previous results it is found that the accretion rate of HD 163296 has increased by more than 1 dex, on a timescale of∼15 yr. Averaged accretion luminosities derived from the Balmer excess are consistent with the ones inferred from the empirical calibrations with the emission line luminosities, indicating that those can be extrapolated to HAe stars. In spite of that, the accretion rate variations do not generally coincide with those estimated from the line luminosities, suggesting that the empirical calibrations are not useful to accurately quantify accretion rate variability.
Key words: accretion, accretion disks – circumstellar matter – line: formation – protoplanetary disks – stars:
pre-main sequence – stars: variables: T Tauri, Herbig Ae/Be Online-only material: color figures
1. INTRODUCTION
The star formation process can be studied from the evolution of the accretion rate (see, e.g., Hartmann1998; Sicilia-Aguilar et al.2004; Fedele et al.2010). At the initial stages, protostars show both envelope-to-disk and disk-to-star accretion, which can show variations of several orders of magnitude on relatively short timescales (FUor and EXor outbursts; e.g., Hartmann
& Kenyon1996; Herbig 2008; Liskowsky2010). During the pre-main-sequence (PMS) phase, once the envelope dissipates and the central object becomes optically visible, the mass accretion rate ( ˙Macc) decreases to typical values of∼10−8 and 10−7M yr−1 for T Tauri (TT) and Herbig Ae/Be (HAeBe) stars, respectively (Hartmann et al. 1998; Mendigut´ıa et al.
2011a,2012). The accretion rate variability in the PMS phase is also expected to be lower than in previous stages. However, the precise strength of those variations is not well known, which can be partly attributed to discrepancies measuring accretion.
Primary signatures of accretion are the excess of UV/optical continuum emission and the veiling in the spectroscopic ab- sorption lines that are observed in accreting stars. Both can be modeled from hot accretion shocks whose emission super- imposes to that of the stellar atmosphere (Calvet & Gullbring 1998). The way that material from the inner disk reaches the stellar surface is understood from the magnetospheric accretion (MA) scenario, according to which gas does not fall directly from the disk to the star but follows the magnetic field lines that connect them (Uchida & Shibata1985; Koenigl1991; Shu et al.
1994). This is the accepted view for TT stars and seems to be valid at least for several HAeBe stars (see, e.g., Vink et al.2002;
Muzerolle et al.2004; Mottram et al.2007; Donehew & Brittain 2011; Mendigut´ıa 2013). Accretion rates obtained from MA shock modeling correlate with the luminosity of several emis- sion lines that span from the ultraviolet (UV) to the infrared (IR; see, e.g., the compilation in Rigliaco et al.2011). These types of empirical calibrations have been extended to late-type HAeBe stars for the [O i] λ6300, Hα (Mendigut´ıa et al.2011a), and Brγ (Donehew & Brittain2011; Mendigut´ıa et al.2011a) lines. The origin of the correlations is not fully understood, but these spectral lines can be considered as secondary signatures of accretion, being useful to easily derive accretion rates for wide samples of stars.
Although some works are based on observed variations of primary accretion signatures in TT stars (e.g., Herbst et al.
1994; Fernandez & Eiroa 1996; Batalha et al. 2001), studies of accretion rate variability are mainly based on secondary ones (e.g., Nguyen et al. 2009; Eisner et al. 2010; Costigan et al.
2012; Chou et al.2013). These analyses provide different results depending on the spectroscopic line used as accretion tracer. As an example, Nguyen et al. (2009) studied a sample of 40 TT stars, reporting typical accretion rate variations of 0.35 dex from the Ca ii λ8862 line flux and 0.65 dex from the Hα 10%. Similar results were more recently obtained by Costigan et al. (2012). In fact, differences in the variability shown by several lines used as accretion tracers are reported for both TT stars and HAeBe stars (Johns & Basri1995; Lago & Gameiro1998; Mendigut´ıa et al.
2011b). However, accretion variability from a primary accretion signature was found to be typically lower than 0.5 dex for the HAeBe stars, on timescales from days to months (Mendigut´ıa et al. 2011a), a result confirmed by Pogodin et al. (2012).
Accretion variability of specific TT stars, determined from line veiling, is also expected to be low (Alencar & Batalha2002).
However, the simultaneous analysis of primary and secondary accretion signatures is necessary to test the reliability of the empirical calibrations between the accretion rate and different spectroscopic lines (Rigliaco et al. 2012), and to study the validity of MA in early-type HAeBe stars (Donehew & Brittain 2011; Mendigut´ıa et al.2011a). These types of studies have been boosted by the advent of the X-Shooter spectrograph at the Very Large Telescope (Vernet et al.2011), which allows simultaneous coverage of the accretion signatures from the UV to the near-IR (NIR). Simultaneity is crucial when dealing with PMS stars, given their variable nature. Several published and ongoing works face those type of questions, by “X-Shooting” wide samples of PMS stars (Oudmaijer et al.2011; Rigliaco et al.
2012; Manara et al.2013).
This work aims to contribute to the understanding of the spectroscopic accretion tracers in HAeBe stars. Instead of relating primary and secondary accretion signatures from single- epoch spectra of large samples, we will analyze multi-epoch spectra of two relevant objects. This approach brings the additional possibility of analyzing the variability of the accretion rate. This paper focuses on the variability behavior of two HAe stars: HD 31648 (MWC 480) and HD 163296. The specific objective is twofold: first, to measure the accretion rate and its variability from the Balmer excess (the primary accretion signature for HAeBe stars, see Garrison1978; Muzerolle et al.
2004); and second, to compare the previous results with several UV, optical, and NIR line luminosities commonly used as secondary accretion tracers in low-mass stars. This comparison will provide relevant information about the applicability of the spectroscopic accretion tracers in late-type HAeBe stars.
The paper is organized as follows: Section 2 describes the observations and data reduction. Section 3 presents our observational results on the Balmer excess (Section3.1) and the spectroscopic lines (Section 3.2). Section 4 includes the analysis of the Balmer excesses in terms of an MA model (Section 4.1) and discusses possible relations between the accretion luminosity derived from the Balmer excess and from the emission line luminosities (Sections4.2and4.3). Finally, Section5summarizes our main conclusions.
2. STARS, OBSERVATIONS, AND DATA REDUCTION HD 31648 and HD 163296 are HAe stars (spectral types A5 and A1, ages of ∼7 Myr and 5 Myr, respectively; Mora et al. 2001; Montesinos et al. 2009) with no reported stellar companions in the literature. We assume the parameters de- rived by Montesinos et al. (2009) for the surface temperature, stellar mass and radius (surface gravity), as well as for the dis- tances (T∗ = 8250 K, 9250 K; M∗ = 2.0 M, 2.2 M; R∗ = 2.3 R, 2.3 R; d= 146 pc, 130 pc; where the first and sec- ond values refer to HD 31648 and HD 163296, respectively).
The stellar luminosities derived in that work are 22 L (HD 31648) and 34.5 L (HD 163296). Both objects show contin- uum and line variations (Sitko et al.2008) and have magnet- ically driven accretion signatures (Swartz et al.2005; Hubrig et al. 2006). We obtained multi-epoch X-Shooter spectra of both objects. Table1 shows the log of the observations. A to- tal of 10 science spectra were taken, 5 spectra per star on a
Table 1
Log of the Observations and Synthetic Photometry
Star Run A Run B Run C Run D Run E
HD 31648 23/10/11 27/10/11 5/11/11 23/02/12 28/02/12 U 8.16± 0.09 8.1 ± 0.2 8.0± 0.1 8.2± 0.1 8.2± 0.2 B 8.18± 0.09 8.0 ± 0.2 8.1± 0.1 8.1± 0.1 8.2± 0.2 V 7.91± 0.09 7.8 ± 0.2 7.8± 0.1 7.8± 0.1 7.9± 0.2 R 7.83± 0.05 7.7 ± 0.2 7.72 ± 0.09 7.73 ± 0.09 7.8 ± 0.2 I 7.65± 0.05 7.5 ± 0.2 7.49 ± 0.09 7.57 ± 0.09 7.6 ± 0.2 J 7.19± 0.09 7.0 ± 0.2 7.1± 0.1 7.2± 0.2 7.3± 0.1 H 6.46± 0.09 6.4 ± 0.2 6.4± 0.1 6.5± 0.2 6.6± 0.1 K 5.70± 0.09 6.1 ± 0.2 5.7± 0.1 5.8± 0.2 5.6± 0.1 HD 163296 12/10/11 14/10/11 16/10/11 24/03/12 17/05/12 U 7.01± 0.09 7.4 ± 0.2 7.2± 0.1 7.4± 0.1 7.3± 0.2 B 7.08± 0.09 7.4 ± 0.2 7.2± 0.1 7.4± 0.1 7.3± 0.2 V 6.90± 0.09 7.2 ± 0.2 7.1± 0.1 7.1± 0.1 7.1± 0.2 R 6.88± 0.05 7.1 ± 0.2 7.03 ± 0.09 7.06 ± 0.09 7.0 ± 0.2 I 6.74± 0.05 7.0 ± 0.2 6.91 ± 0.09 6.92 ± 0.09 6.9 ± 0.2 J 6.21± 0.05 6.4 ± 0.2 6.37 ± 0.09 6.32 ± 0.09 6.1 ± 0.2 H 5.39± 0.05 5.5 ± 0.2 5.50 ± 0.09 5.37 ± 0.09 5.2 ± 0.2 K 4.52± 0.05 4.3 ± 0.2 4.30 ± 0.09 4.18 ± 0.09 4.7 ± 0.2 Notes. Observing dates (dd/mm/yy) and synthetic photometry, in magnitudes, obtained by convolving Johnson–Cousins UBVRI (Bessell 1979) and JHK (Cohen et al.2003) filter passbands with each flux-calibrated spectrum.
timescale from days to months. X-Shooter covers a wide wave- length region throughout its three arms: UVB (311–558 nm), VIS (558–1012 nm), and NIR (1012–2475 nm). The slit widths were 1.6, 0.9, and 0.9, which translates into spectral resolu- tions of 3300, 8800, and 5600 for the UVB, VIS, and NIR arms. The spectra were bias and flat-field corrected and flux and wavelength calibrated from standard procedures using the X-Shooter pipeline v1.5.0 (Modigliani et al.2010). Atmospheric emission was subtracted from an ABBA dithering pattern. Addi- tional telluric absorption correction was applied for specific lines in the NIR arm (Paγ and Brγ ; see Section3.2), by using telluric standards that were observed before and after the target stars.
Flux calibration was tested from low-resolution spectra—i.e., obtained with the widest slit available for all arms (5)—taken consecutively for the target stars and several telluric standard main-sequence objects with similar airmasses. Synthetic pho- tometry obtained by convolving the spectra with broadband UBVRIJHK photometric filters was compared to published val- ues for the telluric standard stars. In this way, the typical uncer- tainty is in between 0.05 and 0.2 mag (flux relative errors∼5%
and 25%), where the specific uncertainties for each star depend on the X-Shooter arm and observing run (see below). Further accuracy could be obtained from spectro-photometric standards, which were not provided. Synthetic photometry extracted from our spectra is included in Table1, which is consistent with previ- ous measurements (de Winter et al.2001; Oudmaijer et al.2001;
Eiroa et al.2001). Flux-calibrated spectra are shown in Figure1.
Values from broadband photometry published in the literature (Oudmaijer et al.2001; Eiroa et al.2001) are overplotted for comparison.
3. OBSERVATIONAL RESULTS 3.1. Balmer Excesses
The Balmer excess is defined from the UB Johnson’s photo- metric bands as ΔDB = (U − B)phot – (U − B)dered, where (U − B)phot is the photospheric color and (U − B)dered the
0 1x10-12 2x10-12 3x10-12 4x10-12 5x10-12 6x10-12
F λ(erg cm-2 s-1 A-1 )
λ (nm)1000 0
2x10-12 4x10-12 6x10-12 8x10-12 1x10-11 1.2x10-11 1.4x10-11
F λ(erg cm-2 s-1 A-1 )
HD 163296 HD 31648
Figure 1. X-Shooter spectra of HD 31648 and HD 163296 in red, green, yellow, blue, and magenta, representing observing runs A, B, C, D, and E, respectively.
Selected broadband photometry and uncertainties taken from the literature are plotted with solid circles and vertical bars. The horizontal bars represent each total filter passband.
(A color version of this figure is available in the online journal.)
observed, dereddened color (Mendigut´ıa et al.2011a). This can be derived from the extinction (in magnitudes), which for a given wavelength can be expressed from that in the V band, or from the B− V color excess, Aλ = AV (kλ/kV) = RVE(B − V ) (kλ/kV). The opacity ratio kλ/kV is known from an extinc- tion law, and RVis the total-to-selective extinction ratio. The X-Shooter UVB spectra were used to measure continuum ex- cesses in the Balmer region, along the different observing runs.
Therefore, the expression for the Balmer excess has been con- verted into fluxes. If the observed ones are normalized to the photospheric emission at the B band (hereafter represented by the superscript “norm, B”), then
ΔDB = 2.5 log
FUnorm,B
FUphot
+ 2.5RV
kU kV −kB
kV
× log
FVnorm,B
FVphot
, (1)
which is the expression that is used in this work. The first term in Equation (1) is essentially the same one as used by Donehew & Brittain (2011), with FUnorm,B/FUphot the ratio between the normalized and the photospheric fluxes, measured at wavelengths corresponding to the U band. The second term reflects the contribution of extinction and can be estimated from an extinction law and from the ratio between the normalized and photospheric fluxes at wavelengths corresponding to the V band. Apart from being independent of absolute flux calibration
(Donehew & Brittain2011), the main advantage of the above expression forΔDB is that it accounts for continuum excesses that can be ascribed mainly to hot shocks caused by accretion (Section4.1), given that the possible contribution of extinction is ruled out by the second term. This contribution is typically an order of magnitude lower than the first term for the stars studied here—their E(B− V ) values are low; see Section3.2—
but it should not be neglected for objects with more pronounced extinctions (i.e., UXOr-like; see, e.g., Grinin et al.1994, and references therein). It is assumed that the third possible cause argued to be in the origin of photometric variability in PMS stars, photospheric variations caused by cold spots (Herbst et al.
1994), is negligible for the stellar temperatures and masses of both stars analyzed. The photospheric fluxes are represented by Kurucz models (Kurucz 1993) with the corresponding values of T∗ and log g (Section 2). These were derived from the SYNTHE code, re-binning to a resolution similar to the X-Shooter spectra, as they were also used to estimate the photospheric contribution to the spectral lines (Section 3.2).
Observed fluxes were normalized to the Kurucz ones, making their averaged continuum fluxes in the 400–460 nm band (representing the rough range covered by the B photometric filter) coincide. The ratios FUnorm,B/FUphot and FVnorm,B/FVphot were then derived considering averaged continuum fluxes in the wavelength regions 350–370 nm and 540–560 nm, respectively.
Balmer excesses were finally obtained from Equation (1), assuming RV= 5 (Hern´andez et al. 2004), kU/kV = 1.6, and kB/kV = 1.3 (Rieke & Lebofsky1985; Robitaille et al.2007).
350 400 450 500 550 λ (nm)
2x107 4x107 6x107 8x107
Normalized flux (erg cm-2 s-1 A-1 ) HD 31648
350 400 450 500 550
λ (nm) 2x107
4x107 6x107 8x107 1x108 1.2x108
Normalized flux (erg cm-2 s-1 A-1 ) HD 163296
Figure 2. X-Shooter UVB spectra of HD 31648 and HD 163296, normalized to Kurucz photospheric spectra at the stellar surface in the 400–460 nm band. Normalized spectra are plotted in different colors representing different observing runs, as in Figure1. Kurucz spectra are plotted with black solid lines.
(A color version of this figure is available in the online journal.)
Table 2 Observed Balmer Excesses
Star ΔDB(Run A) ΔDB(Run B) ΔDB(Run C) ΔDB(Run D) ΔDB(Run E) ΔDB
(mag) (mag) (mag) (mag) (mag) (mag)
HD 31648 0.15 0.12 0.18 0.07 0.18 0.14 [0.33]
HD 163296 0.37 0.38 0.41 0.38 0.36 0.38 [0.04]
Notes. Observed Balmer excesses are shown in Columns 2–6. The typical uncertainty is 0.01 mag. The last column shows the mean Balmer excess and a number in brackets quantifying the relative variability.
The use of a larger RVvalue, compared with the typical value for the interstellar medium (RV = 3.1), has been extensively justified for HAeBe stars (see, e.g., Herbst et al.1982; Gorti
& Bhatt1993; Hern´andez et al.2004; Manoj et al.2006, and references therein). In addition, interstellar extinction is most likely negligible compared with the circumstellar one for objects located closer than 200 pc (Fitzgerald1968), as is the case for HD 31648 and HD 163296. A different RVvalue than assumed here affects the second term in Equation (1). In particular, RV= 3.1 provides Balmer excesses that can be lower by 0.08 mag, this upper limit being obtained from specific observing runs of HD 163296. For simplicity, possible variations of RVfor a given star, or strong dependences of the extinction law on RV, are not considered for the low extinctions and the wavelength range covered in this work (Mathis1990).
Figure2shows the observed spectra for the two stars studied here, normalized to the Kurucz ones at wavelengths correspond- ing to the B photometric filter. Balmer excesses with respect to the photospheric spectra are apparent in the 350–370 nm re- gion, and those can vary from one epoch to another. Table2 shows the measured ΔDB values. Apart from the extinction law, the uncertainty of the Balmer excesses is only dependent on relative flux ratios in wavelengths corresponding to the U and V photometric filters (see Equation (1)). In other words, the accuracy of the Balmer excess would only decrease if er- rors in flux calibration are strongly wavelength dependent in the 350–560 nm region, which is not the case for our spectra. A con- servative uncertainty of 0.01 mag was estimated by measuring (the theoretically null)ΔDB in consecutive X-Shooter spectra of main-sequence stars on different observing dates and with different airmasses, for which neither accretion nor changes in extinction were present. The last column in Table2shows the mean Balmer excess and its relative variability, σ (ΔDB)/ΔDB, defined as the ratio between the standard deviation and the av-
erage Balmer excess from the different observing runs. While HD 163296 shows the largest mean Balmer excess (0.41 mag), HD 31648 shows the largest Balmer excess variations (up to a factor of 2.5 in a few days). The importance of the second term in Equation (1) is noted again: despite the similar variability shown in the Balmer region of the spectra in both panels of Figure2, the contribution of (variable) extinction to this vari- ability is a bit more pronounced in HD 163296 (its normalized flux shows larger differences with respect to the Kurucz model at longer wavelengths).
3.2. Spectral Lines
This work focuses on 12 emission lines for which there are previous empirical calibrations with the accretion luminosity in the literature (Section4.2). These lines span over the whole UVB-VIS-NIR wavelength region covered by the X-Shooter spectra. In particular, we focused on transitions of neutral hy- drogen, helium, sodium, and oxygen, also including transitions of ionized calcium. Figure3 shows the observed line profiles of HD 31648 and HD 163296, along the five observing runs.
Forbidden emission lines most probably tracing outflow pro- cesses ([O i], [S ii], [Fe i]) were not detected in any of the spectra. However, both stars show variable blueshifted self- absorptions in several lines (Hα, Ca ii λ8542, Paβ), as well as variable redshifted self-absorptions in others (Ca ii K, Hβ, O i λ8446). Several works deal with the physical origin of some of these lines (see, e.g., Hartmann et al.1994; Muzerolle et al. 1998,2001, 2004; Tambovtseva et al. 1999; Kurosawa et al.2006), which have been associated mainly with accretion and/or outflow processes. The study of the physical origin of the spectral lines is beyond the scope of this work.
The circumstellar contribution to the equivalent width (EW) of a line was determined from EWcs = EWobs − EWphot. The observed equivalent width, EWobs, was directly measured
-2000 -1000 0 1000 2000 0.2
0.4 0.6 0.8 1 1.2
-1000 -500 0 500 1000 0
0.2 0.4 0.6 0.81 1.2 1.4 1.6
HD 31648
-3000 -1500 0 1500 3000 0
0.2 0.4 0.6 0.8 1 1.2
-4000 -2000 0 2000 4000 0.20
0.40.6 0.81 1.21.4 1.61.8
-1500 -1000 -500 0 500 0.4
0.6 0.8 1 1.2
-1500-1000 -5000 0 500 1000 1500 1
2 3 4 5
-750 -500 -250 0 250 500 750 0.95
1 1.05 1.1 1.15
Relative intensity
-750 -500 -250 0 250 500 750 1
1.5 2 2.5 3
-2000 -1000 0 1000 2000
0.8 1 1.2 1.4 1.6
-750 -500 -250 0 250 500 750 1
1.5 2 2.5
-750 -500 -250 0 250 500 750
v (km s-1)
0.9 1 1.1 1.2 1.3 1.4 1.5
Hη3835 CaIIK3934 Hγ4341
Hβ4861 HeI5876&NaID5893 Hα6563
a P 2
4 5 8 I I a
C γ10938
Brγ21660 Paβ12818
OI8446
-2000 -1000 0 1000 2000 0.2
0.4 0.6 0.8 1 1.2
-1000 -500 0 500 1000
0.4 0.6 0.8 1 1.2 1.4
HD 163296
-3000 -1500 0 1500 3000 0.2
0.4 0.6 0.8 1 1.2
-2000 0 2000
0.2 0.4 0.6 0.8 1 1.2 1.4
-1500 -1000 -500 0 500 1000 0.9
1 1.1 1.2
-2000 -1000 0 1000 2000 1
2 3 4
-900 -600 -300 0 300 600 900 1
1.05 1.1 1.15
Relative intensity
-750 -500 -250 0 250 500 750 1
1.2 1.4 1.6 1.8 2
-800 -400 0 400 800 1
1.2 1.4 1.6
-750 -500 -250 0 250 500 750 1
1.5 2
-500 -250 0 250 500
v (km s-1)
0.9 1 1.1 1.2 1.3
Hη3835 CaIIK3934 Hγ4341
Hβ4861 HeI5876&NaID5893 Hα6563
a P 2
4 5 8 I I a
C γ10938
Brγ21660 Paβ12818
OI8446
Figure 3. Observed line profiles (normalized to unity) of HD 31648 and HD 163296 are shown with solid lines. Different colors represent different observing runs, as in Figure1. For the UV lines with a purely absorption profile (Hη, Ca ii K, Hγ , and Hβ), the emission profiles (dashed lines) that result from the subtraction of the Kurucz synthetic spectra (solid black lines) from the observed ones are also shown (see text).
(A color version of this figure is available in the online journal.)
Table 3 Line Equivalent Widths
Line EWphot EWcs EWcs EWcs EWcs EWcs
(Run A) (Run B) (Run C) (Run D) (Run E) EWcs
(Å) (Å) (Å) (Å) (Å) (Å) (Å)
HD 31648
Hη (3835 Å) 10.4 −1.0 ± 0.1 −1.7 ± 0.1 −0.7 ± 0.7 0.1± 0.7 −1.4 ± 0.8 −1.2 [0.60]
Ca ii K (3934 Å) 4.5 −1.1 ± 0.2 −0.2 ± 0.1 −1.2 ± 0.1 −0.7 ± 0.1 −1.9 ± 0.2 −1.0 [0.65]
Hγ (4341 Å) 23.6 −4 ± 3 −3 ± 2 −5 ± 3 −3 ± 2 −3 ± 3 −3 ± 1
Hβ (4861 Å) 34.5 −18 ± 2 −17 ± 2 −19 ± 2 −19 ± 2 −19 ± 2 −18 ± 1
He i (5876 Å) 0.02 −1.3 ± 0.4 −1.2 ± 0.4 −0.8 ± 0.4 −0.8 ± 0.4 −1.0 ± 0.3 −1.0 ± 0.2
Na i D2(5890 Å) 0.26 −0.57 ± 0.06 0.09± 0.05 −0.23 ± 0.08 0.25± 0.06 −0.94 ± 0.06 −0.58 [0.84]
Na i D1(5896 Å) 0.19 −0.60 ± 0.09 −0.06 ± 0.06 −0.35 ± 0.07 −0.07 ± 0.07 −0.70 ± 0.06 −0.36 [0.80]
Hα (6563 Å) 21.5 −25.6 ± 0.1 −23.6 ± 0.1 −28.3 ± 0.2 −25.5 ± 0.2 −25.0 ± 0.1 −25.6 [0.07]
O i (8446 Å) 0.26 −1.3 ± 0.2 −1.0 ± 0.2 −1.4 ± 0.2 −1.1 ± 0.2 −1.1 ± 0.2 −1.1 ± 0.1
Ca ii (8542 Å) 3.5 −13.9 ± 0.3 −9.2 ± 0.2 −15.2 ± 0.3 −10.7 ± 0.3 −13.0 ± 0.3 −12.4 [0.20]
Paγ (10938 Å) 24.9 −26 ± 1 −23 ± 1 −27 ± 1 −22 ± 1 −24 ± 1 −25 [0.08]
Paβ (12818 Å) 22.8 −36.0 ± 0.6 −32.0 ± 0.5 −37.1 ± 0.6 −34.6 ± 0.6 −36.0 ± 0.6 −35.1 [0.06]
Brγ (21660 Å) 26.3 −33.2 ± 0.6 −31.3 ± 0.7 −34.3 ± 0.6 −32.9 ± 0.7 −33.1 ± 0.7 −33.0 [0.03]
HD 163296
Hη (3835 Å) 10.4 −0.3 ± 0.4 0.1± 0.4 −0.2 ± 0.3 −0.4 ± 0.3 −0.2 ± 0.4 −0.3 ± 0.2
Ca ii K (3934 Å) 2.7 −0.3 ± 0.1 0.4± 0.1 −0.52 ± 0.09 −0.50 ± 0.09 −0.76 ± 0.08 −0.34 [1.3]
Hγ (4341 Å) 23.2 −1 ± 3 0± 3 −2 ± 3 −3 ± 3 −1 ± 3 −2 ± 1
Hβ (4861 Å) 29.2 −12 ± 1 −12.4 ± 0.8 −12 ± 1 −13 ± 1 −12 ± 2 −12.5 ± 0.6
He i (5876 Å) 0.03 −0.7 ± 0.1 −0.5 ± 0.3 −0.8 ± 0.2 −0.3 ± 0.3 −0.8 ± 0.3 −0.7 ± 0.1
Na i D2(5890 Å) 0.16 −0.8 ± 0.1 −0.34 ± 0.07 −0.51 ± 0.07 −0.70 ± 0.07 −0.53 ± 0.08 −0.58 [0.33]
Na i D1(5896 Å) 0.14 −0.8 ± 0.1 −0.36 ± 0.09 −0.62 ± 0.08 −0.57 ± 0.07 −0.87 ± 0.09 −0.64 [0.31]
Hα (6563 Å) 30.2 −35 ± 4 −30 ± 4 −33 ± 3 −34 ± 3 −33 ± 4 −33 ± 2
O i (8446 Å) 0.24 −1.3 ± 0.2 −0.8 ± 0.1 −1.4 ± 0.3 −1.4 ± 0.3 −1.1 ± 0.2 −1.2 [0.23]
Ca ii (8542 Å) 3.1 −9.1 ± 0.4 −5.2 ± 0.9 −8.5 ± 0.3 −9.7 ± 0.4 −8.4 ± 0.3 −8.2 [0.21]
Paγ (10938 Å) 23.2 −23 ± 1 −24 ± 1 −24 ± 1 −26.3 ± 0.6 −23 ± 1 −24.0 [0.05]
Paβ (12818 Å) 20.7 −31.3 ± 0.7 −28.1 ± 0.7 −28.8 ± 0.7 −31.1 ± 0.9 −29.5 ± 0.7 −29.8 [0.05]
Brγ (21660 Å) 22.2 −27.0 ± 0.4 −25.6 ± 0.4 −26.2 ± 0.6 −25.8 ± 0.5 −25.7 ± 0.5 −26.0 [0.02]
Notes. Photospheric and circumstellar equivalent widths are shown in Columns 2–7. The last column shows the mean equivalent width and its uncertainty from the propagation of the individual ones. For the stars showing both absorptions and emissions, only the values of the most frequent absorption/emission behavior are considered to derive the mean values. A number in brackets quantifying the relative variability (σ (EWcs)/EWcs) is provided when the equivalent width varies above the uncertainties.
on the normalized spectra,8 whereas the photospheric absorp- tion, EWphot, was estimated from the Kurucz spectra with the corresponding stellar parameters (see Section3.1). These pro- files were broadened by stellar rotation, assuming projected rotational velocities of 133 and 102 km s−1for HD 163296 and HD 31648, respectively (Mora et al.2001). For the resolution of our X-Shooter spectra, variations of 500 K in the stellar tem- perature and changes of 0.50 dex in the surface gravity of the Kurucz spectra (uncertainties of ±200 K and ±0.2 dex were quoted in Montesinos et al.2009) translate into typical relative errors of 10% and 5% in EWphot(the specific values depending on the specific star and line). However, since we are mainly interested in the variability of the lines and the photospheric contribution is expected to be constant, it is assumed that the uncertainty in EWcs is dominated by that in EWobs. This was determined for each individual line and observing run by mea- suring additional EWs from two levels located at±1.5σ from the normalized continuum, fixed at unity. Table 3 shows the equivalent widths and the errors estimated in this way. The rel- ative variability, σ (EWcs)/EWcs (see, e.g., Mendigut´ıa et al.
2011b), is indicated in those cases where the EW changes above the uncertainties.
8 The entire line, considering both the emission and absorption components, is taken for this measurement.
Dereddened line luminosities (Lderedλ ) were obtained from the values for EWcs, the observed continuum fluxes at wavelengths close to the lines (Fcont,λobs ), and the distances to the stars (d). We used the expression Lderedλ = 4πd2 × Fλdered, where Fλdered = EWcs×Fcont,λdered = EWcs×Fcont,λobs × 100.4Aλ. The extinction, Aλ= RVE(B − V )(kλ/kV), was derived assuming again RV = 5, and from the kλ/kV values in Rieke & Lebofsky (1985) and Robitaille et al. (2007). (B− V ) color excesses were obtained subtracting the corresponding magnitudes extracted from the Kurucz spectra from the ones included in Table 1. These are shown in Table4, along with the dereddened line luminosities and their uncertainties (which consider those in the EW and in Fcont,λobs ), as well as the relative variability when a line shows luminosity variations above the uncertainties.
Although line luminosities tend to be larger for HD 163296, the variability of the lines, in terms of both the EWs and the line luminosities, is comparable for HD 31648 and HD 163296.
4. ANALYSIS AND DISCUSSION 4.1. Accretion Rates from Balmer Excesses
It is assumed that accretion is magnetically channeled for the two stars studied in this paper. Therefore, the observed Balmer excesses and their variations (Section3.1) are analyzed
Table 4
Dereddened Line Luminosities
Line log L/L log L/L log L/L log L/L log L/L
(Run A) (Run B) (Run C) (Run D) (Run E) logL/L
HD 31648
E(B− V ) 0.08 0.09 0.10 0.13 0.09
Hη (3835 Å) −2.3 ± 0.4 −2.0 ± 0.2 <−2.07 <−2.38 −2.1 ± 0.3 −2.1 ± 0.2
Ca ii K (3934 Å) −2.22 ± 0.09 −2.9 ± 0.3 −2.07 ± 0.06 −2.3 ± 0.1 −2.0 ± 0.1 −2.19 [0.57]
Hγ (4341 Å) −1.8 ± 0.4 −1.8 ± 0.4 −1.6 ± 0.3 −1.8 ± 0.3 <−1.52 −1.7 ± 0.2
Hβ (4861 Å) −1.21 ± 0.06 −1.2 ± 0.1 −1.10 ± 0.06 −1.03 ± 0.06 −1.2 ± 0.1 −1.13 [0.16]
He i (5876 Å) −2.6 ± 0.1 −2.6 ± 0.2 −2.7 ± 0.2 −2.7 ± 0.2 −2.7 ± 0.2 −2.6 ± 0.1
Na i D2(5890 Å) −2.95 ± 0.05 · · · −3.3 ± 0.2 · · · −2.71 ± 0.09 −2.92 [0.60]
Na i D1(5896 Å) −2.94 ± 0.07 · · · −3.09 ± 0.09 · · · −2.83 ± 0.09 −2.94 [0.28]
Hα (6563 Å) −1.43 ± 0.02 −1.4 ± 0.1 −1.31 ± 0.04 −1.31 ± 0.04 −1.41 ± 0.09 −1.37 [0.13]
O i (8446 Å) −3.01 ± 0.07 −3.1 ± 0.1 −2.89 ± 0.07 −2.99 ± 0.09 −3.1 ± 0.1 −3.00 [0.17]
Ca ii (8542 Å) −1.97 ± 0.02 −2.1 ± 0.1 −1.86 ± 0.04 −1.99 ± 0.04 −1.97 ± 0.09 −1.97 [0.19]
Paγ (10938 Å) −1.96 ± 0.04 −2.0 ± 0.1 −1.86 ± 0.05 −2.0 ± 0.1 −1.99 ± 0.05 −1.94 [0.11]
Paβ (12818 Å) −1.93 ± 0.04 −1.9 ± 0.1 −1.87 ± 0.05 −1.9 ± 0.1 −1.95 ± 0.04 −1.91 ± 0.03
Brγ (21660 Å) −2.28 ± 0.04 −2.5 ± 0.1 −2.29 ± 0.05 −2.4 ± 0.1 −2.22 ± 0.04 −2.32 [0.23]
HD 163296
E(B− V ) 0.10 0.13 0.10 0.16 0.15
Hη (3835 Å) <−2.06 <−2.48 <−2.28 −2.3 ± 0.4 <−2.27 −2.3 ± 0.4
Ca ii K (3934 Å) −2.4 ± 0.2 · · · −2.18 ± 0.09 −2.09 ± 0.09 −1.9 ± 0.1 −2.11 [0.41]
Hγ (4341 Å) <−1.31 <−1.47 <−1.28 <−1.10 <−1.28 . . .
Hβ (4861 Å) −1.00 ± 0.05 −1.0 ± 0.1 −1.06 ± 0.06 −0.91 ± 0.05 −1.0 ± 0.1 −0.99 [0.13]
He i (5876 Å) −2.52 ± 0.06 −2.8 ± 0.3 −2.5 ± 0.1 <−2.57 −2.5 ± 0.2 −2.6 ± 0.1
Na i D2(5890 Å) −2.47 ± 0.06 −2.9 ± 0.1 −2.75 ± 0.07 −2.52 ± 0.06 −2.6 ± 0.1 −2.63 [0.38]
Na i D1(5896 Å) −2.49 ± 0.06 −2.9 ± 0.2 −2.66 ± 0.07 −2.61 ± 0.07 −2.4 ± 0.1 −2.58 [0.37]
Hα (6563 Å) −0.99 ± 0.05 −1.1 ± 0.1 −1.07 ± 0.06 −0.98 ± 0.05 −1.0 ± 0.1 −1.02 ± 0.04
O i (8446 Å) −2.71 ± 0.07 −3.0 ± 0.1 −2.8 ± 0.1 −2.7 ± 0.1 −2.8 ± 0.1 −2.76 [0.26]
Ca ii (8542 Å) −1.86 ± 0.03 −2.2 ± 0.1 −1.96 ± 0.04 −1.83 ± 0.04 −1.88 ± 0.09 −1.92 [0.26]
Paγ (10938 Å) −1.73 ± 0.03 −1.8 ± 0.1 −1.79 ± 0.04 −1.67 ± 0.04 −1.66 ± 0.09 −1.73 [0.15]
Paβ (12818 Å) −1.71 ± 0.02 −1.8 ± 0.1 −1.80 ± 0.04 −1.69 ± 0.04 −1.66 ± 0.09 −1.73 [0.15]
Brγ (21660 Å) −2.00 ± 0.02 −1.9 ± 0.1 −1.90 ± 0.04 −1.84 ± 0.04 −2.13 ± 0.09 −1.94 [0.24]
Notes. Emission line luminosities in Columns 2–6 are dereddened using the color excesses indicated on the top of each column (in magnitudes) and a distance of 146 and 130 pc for HD 31648 and HD 163296, respectively. The last column shows the mean line luminosity and its uncertainty from the propagation of the individual ones. A number in brackets quantifying the relative variability (σ (L)/L) is provided when the line luminosity varies above the uncertainties. Upper limits are not considered to derive mean and relative variability values. Blank spaces refer to lines shown in absorption.
in terms of an MA shock model. We follow the nomenclature and methodology described in Mendigut´ıa et al. (2011a), where several assumptions of the MA shock model in Calvet &
Gullbring (1998) and Muzerolle et al. (2004) were applied to HAeBe stars. According to that, the total flux per wavelength unit emerging from the star (Fλ) is composed of the emission from the naked photosphere (Fλphot, represented by a Kurucz synthetic spectrum) plus the accretion contribution:
Fλ= fFcolλ + (1− f )Fλphot, (2) f being the filling factor that reflects the stellar surface coverage of the accretion columns, and Fλcol the flux from the column.
This parameter is modeled as a blackbody at a temperature Tcol= [F/σ + T∗4]1/4, (3) with σ the Stefan–Boltzmann constant andF the inward flux of energy carried by the accretion columns, which ranges typically between 1011 and 1012 erg cm−2 s−1 (Muzerolle et al.2004).
The filling factor can be estimated from f =
1−R∗
Ri
GM∗˙Macc
4πFR3∗ , (4)
with Rithe disk truncation radius.
Table 5 Fixed Model Parameters
Parameter Symbol (units) HD 31648 HD 163296
Stellar temperature T∗(K) 8250 9250
Stellar mass M∗(M) 2.0 2.2
Stellar radius R∗(R) 2.3 2.3
Accretion column flux F (erg cm−2s−1) 1012 1012
Disk truncation radius Ri(R∗) 2.5 2.2
Table5summarizes the fixed input parameters that are used in this work. Figure 4 shows the average UV spectrum of HD 163296 normalized to the Kurucz photospheric spectrum in the B band. For a typical accretion rate of∼10−7Myr−1and fixed stellar parameters and disk truncation radius (see below), different values ofF provide different blackbody temperatures (Equation (3)) and filling factors (Equation (4)). The cor- responding total fluxes (Equation (2)) reproduce the ob- served spectra with different degrees of accuracy. For F ∼ 1011erg cm−2s−1, the only part of the observed spectrum that can be reproduced is the bump between 365 and 370 nm, mis- matching at shorter and longer wavelengths (λ > 380 nm).
Values ofF ∼ 1012erg cm−2s−1are able to reasonably repro- duce both the short- and long-wavelength regions. Larger values
Figure 4. Average UV spectrum of HD 163296 (black dotted line) normalized to the Kurucz synthetic spectrum (black solid line) at the B band. The colored dotted lines refer to modeled spectra with fixed mass accretion rate (10−7Myr−1), stellar parameters, and disk truncation radius (see text), but different values for the inward flux energy,F, as indicated in the legend. Those values are associated with different blackbody temperatures and filling factors by Equations (3) and (4):∼9700 K (f ∼ 20%), 12500 K (f ∼ 2%), and 25,000 K (f ∼ 0.1%) for the red, green, and blue lines, respectively.
(A color version of this figure is available in the online journal.)
(F ∼ 1013erg cm−2s−1) are not able to reproduce any part of the observed Balmer excesses. As it is described in the follow- ing, our modeling aims to reproduce mainly the strength of the observed Balmer excess, instead of its overall shape. We as- sume a “classical” approach using a single blackbody obtained by fixingF to 1012erg cm−2s−1, which not only provides rea- sonable agreement with the observed excesses and filling factors (Valenti et al.1993), but is in turn the typical value for HAe stars (Muzerolle et al.2004). More complex models using several values ofF have been used to simultaneously reproduce wider wavelength ranges covering the near-UV and optical regions of T Tauri stars (see, e.g., Ingleby et al.2013). Disk truncation radii assumed in this work (Table5) are also typical (Muzerolle et al. 2004), being lower than the corresponding co-rotation radii (Shu et al.1994) by taking into account the projected rota- tional velocities of the stars (Mendigut´ıa et al.2011a). We refer the reader to this paper for further details on the shock mod- eling and its dependences on the stellar parameters. Although already discussed there, further analysis on the influence of the adopted values for F and Ri is included below. Total fluxes were synthesized from Equation (2) for each star, considering different values for ˙Macc. Modeled Balmer excesses were then derived by normalizing Fλ to Fλphot in the 400–460 nm band and applying the same procedure as described for the observed Balmer excesses (Section3.1). In this way, couples of values ( ˙Macc,ΔDB) were obtained for each star, which were used to construct the curves represented in Figure5. TheseΔDB– ˙Macc calibrations were used to assign a mass accretion rate to each observed Balmer excess. Accretion luminosities were then de- rived considering Lacc= GM∗M˙acc/R∗. The model parameters that best reproduce the values of the observed Balmer excesses are shown in Table6. The uncertainties for ˙Maccwere estimated considering the typical uncertainty for the observed Balmer ex- cess (±0.01 mag; see Section3.1) in theΔDB– ˙Macccalibration (Figure5). Errors in M∗/R∗ratios (Montesinos et al.2009) add another 0.01 dex uncertainty to the accretion luminosities (see Mendigut´ıa et al.2011a, and the caption of Table6).
From the method described before, the mean mass accre- tion rate for HD 31648 was 1.11× 10−7Myr−1. The accre-
-7.4 -7.2 -7 -6.8 -6.6 -6.4 -6.2 -6 log Macc (Msun yr-1)
0.1 0.15 0.2 0.25 0.3 0.35 0.4
ΔD B (mag)
Figure 5. Calibration between the Balmer excess and the mass accretion rate for HD 31648 (solid line) and HD 163296 (dashed line). The observed Balmer excesses are over plotted with filled and open circles. The uncertainty in the observed Balmer excesses is represented by the black vertical bar.
Table 6
Accretion Parameters from the Observed Balmer Excesses
Star Run log ˙Macc log Lacc f
[Myr−1] [L] (%)
A −6.92 0.51 2.3
B −7.03 0.40 1.8
HD 31648 C −6.84 0.60 2.8
(Tcol= 12,215 K) D −7.28 0.15 1.0
E −6.84 0.60 2.8
A −6.36 1.11 8.5
B −6.35 1.13 8.8
HD 163296 C −6.31 1.17 9.7
(Tcol= 12,570 K) D −6.35 1.13 8.8
E −6.38 1.10 8.2
Notes. Uncertainties for log ˙Maccand log Laccare±0.03 dex and ±0.04 dex (for HD 31648) and±0.02 dex and ±0.03 dex (for HD 163296).
tion rate changes are above the uncertainties, between 5.24× 10−8M yr−1 and 1.46 × 10−7M yr−1. This represents a mass accretion rate variation of almost 0.5 dex. The accretion luminosity showed an average value of 3.03 L and changes by a factor of almost 3, from 1.43 to 3.97 L. This repre- sents accretion luminosity variations between 6.5% and 18%
of the stellar one. Regarding HD 163296, the mass accretion rate was typically larger (∼4.50 × 10−7Myr−1) and roughly constant (variations lower than 0.1 dex). The accretion lumi- nosity was typically∼40% of the stellar one. Despite this high ratio, significant veiling in photospheric absorption lines is not detected, which is consistent with a temperature of the accretion shocks similar to the effective temperature of the star (Muzerolle et al.2004).
The above discussion assumes that the fraction of the star covered by the shocks, f, is the only model parameter that varies along the observations. This assumption provides upper limits for the accretion rate changes. In other words, more complex scenarios assuming additional variations in F and Ri would explain a given Balmer excess change from a lower accretion rate variation than provided here. As an example, in the case of HD 31648 a change of 20% inF and Riwould account for Balmer excess variations of 0.2 and 0.4 mag, respectively, for a fixed accretion rate of 1.11× 10−7M yr−1. Further analysis
-2.5 -2.25 -2 -0.5 0.5 1.5 2.5 0 2 3 1
-3 -2.75 -2.5 -2.25 -2 -1.75 -1.5 -1.25
-1.25 -1
-0.5 0.5 1.5 2.5 0 2 3 1
-3.25 -3 -2.75 -2.5 -2.75 -2.5 -2.25
-1.5 -1.25 -1
-0.5 0.5 1.5 2.5 0 2 3 1 lo g (L
acc/L
sun)
-3 -2.75 -2 -1.75
-2 -1.75
-0.5 0.5 1.5 2.5 0 2 3 1
-2 -1.75
log (L
line/L
sun)
-2.5 -2.25 -2 -1.75
Hη3835 CaIIK3934 Hγ4341
Hβ4861 HeI5876 NaID5893
Hα6563 OI8446 CaII8542
Paγ10938 Paβ12818 Brγ21660
Figure 6. Accretion luminosities from the Balmer excess versus emission line luminosities for HD 31648 (filled symbols) and HD 163296 (open symbols). Left- pointing triangles represent upper limits for the line luminosities. Upper limits for the accretion luminosity obtained∼15 yr ago (see text) are plotted with big triangles (filled and open for HD 31648 and HD 163296, respectively), with respect to contemporaneous He i λ5876, Na i D, and Hα luminosities. Empirical calibrations from previous works (Calvet et al.2004; Dahm2008; Gatti et al.2008; Herczeg & Hillenbrand2008; Fang et al.2009; Mendigut´ıa et al.2011a) and±1 dex uncertainties are indicated with solid and dashed lines, respectively.
in this sense is out of the scope of this work. However, it should be mentioned that changes in the disk truncation radius are considered in 3D simulations of MA (Kulkarni & Romanova 2013). In addition, given that there are observed variations in the ratio of the Balmer lines (which is a probe of the density ρ), especially in the case of HD 31648, it may be likely that the density of material in the columns is varying. Given that F ∝ ρv3, with v the velocity of the infalling material (see, e.g., Calvet & Gullbring1998), a change in the Balmer ratio could be indicating variations inF.
4.2. Accretion Rates and Line Luminosities
The accretion luminosities derived from the Balmer excesses are plotted against the dereddened line luminosities in the different panels of Figure6. Empirical calibrations relating both parameters were taken from the literature (see below) and are overplotted with solid lines. These have the form log Lacc/L= a log Lline/L + b, a and b being constants that depend on the spectral line. These relations were calibrated by relating primary accretion signatures (i.e., line veiling or continuum excess) with the line luminosities and show a typical maximum
scatter of∼±1 dex, which is represented by the dashed lines.
The calibration obtained from HAeBe stars in Mendigut´ıa et al.
(2011a) is overplotted in the Hα panel. This is very similar to the corresponding relation for lower mass T Tauri stars and brown dwarfs (Dahm2008; Herczeg & Hillenbrand2008). The relation derived by Calvet et al. (2004) (see also Donehew & Brittain 2011; Mendigut´ıa et al.2011a) is used for the Brγ panel. That was based on intermediate-mass TT stars (F and G spectral types and masses up to 4 M). For the remaining lines there are no Lacc–Lline relations calibrated from HAeBe stars. The empirical relations for the He i λ5876, Ca ii 8542, and Paβ are from Dahm (2008), based on objects with masses up to 2 M. The calibrations with the rest of the lines were derived from objects with masses below 1 Mand were taken from Herczeg
& Hillenbrand (2008; Hη, Ca ii K, Hγ , Na i D, O i λ8446), Gatti et al. (2008; Paγ ), and Fang et al. (2009; Hβ).
The accretion and line luminosities plotted in Figure6 fall within the range expected from previous Lacc–Lline calibra- tions. This suggests that these relations, mostly derived from low-mass stars, can be extrapolated to provide accretion rate estimates for HAe stars. However, the fact that HD 31648 and HD 163296 show different Balmer excess—accretion
